81/64: Difference between revisions

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The '''Pythagorean major third''', '''81/64''', may be reached by stacking four perfect fifths ([[3/2]]), and reducing by two [[octave]]s.  In contrast to the more typical [[5/4]]- with which it is conflated in [[meantone]]- this interval is a bit more dissonant when not bridged by a stack of 3/2 within in a chord, with a [[harmonic entropy]] level somewhere between that of [[9/8]] and that of [[8/7]].  Thus, some would argue that it is functionally an imperfect dissonance.
The '''Pythagorean major third''', '''81/64''', may be reached by stacking four perfect fifths ([[3/2]]), and reducing by two [[octave]]s.  In contrast to the more typical [[5/4]]- with which it is conflated in [[meantone]]- this interval is a bit more dissonant when not bridged by a stack of 3/2 intervals within in a chord, with a [[harmonic entropy]] level somewhere between that of [[9/8]] and that of [[8/7]].  Thus, some would argue that it is functionally an imperfect dissonance.


== See also ==
== See also ==

Revision as of 17:47, 4 November 2021

Interval information
Ratio 81/64
Factorization 2-6 × 34
Monzo [-6 4
Size in cents 407.82¢
Name Pythagorean major third
Color name Lw3, lawa 3rd
FJS name [math]\displaystyle{ \text{M3} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 12.3399
Weil norm (log2 max(n, d)) 12.6797
Wilson norm (sopfr(nd)) 24

[sound info]
Open this interval in xen-calc

The Pythagorean major third, 81/64, may be reached by stacking four perfect fifths (3/2), and reducing by two octaves. In contrast to the more typical 5/4- with which it is conflated in meantone- this interval is a bit more dissonant when not bridged by a stack of 3/2 intervals within in a chord, with a harmonic entropy level somewhere between that of 9/8 and that of 8/7. Thus, some would argue that it is functionally an imperfect dissonance.

See also